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Statistical Inference for Irregularly Observed Processes

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Time Series Analysis of Irregularly Observed Data

Part of the book series: Lecture Notes in Statistics ((LNS,volume 25))

Abstract

1. Statistical Inference. Statistics is part of the methodology of science—pure and applied. It is pertinent to the various goals of science proper: explanation and understanding, prediction and control, discovery and application, justification, classification. Various writers have set down block diagrams illustrating how scientific enquiry proceeds and how statistics impinges on that process. We mention Bartlett (1967), Box (1976), Mohr (1977) and Parzen (1980). An early writerwas Kempthorne (1952) who set down (essentially) the following diagram.

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References

  • Akaike, H. (1980). Likelihood and the Bayes procedure. In Bayesian Statistics (Eds. J. M. Bernado, M. H. DeGroot, D. V. Lindley and A. F. M. Smith), University Press, Valencia, pp. 141–166.

    Google Scholar 

  • Allison, H. (1979). Inverse unstable problems and some of their applications. Math. Scientist 4, 9–30.

    Google Scholar 

  • Bartlett, M. S. (1966). Stochastic Processes. University Press, Cambridge.

    MATH  Google Scholar 

  • Bartlett, M.S. (1967). Inference and stochastic processes. J. R. Statist. Soc. A 130, 457–477.

    Article  Google Scholar 

  • Bloomfield, P. (1970). Spectral analysis with randomly missing observations. J. R. Statist. Soc. B 32, 369–380.

    MathSciNet  MATH  Google Scholar 

  • Box, G. E. P. (1976). Science and statistics. J. Amer. Statist. Assoc. 71, 791–799.

    MathSciNet  MATH  Google Scholar 

  • Breiman, L., Dixon, W., Azen, S. and Hill, M. (1981). Missing value problems in multiple regression. Proc. Amer. Statist. Assoc. Annual Meeting.

    Google Scholar 

  • Bretherton, F. P. and McWilliams, J. C. (1980). Estimations from irregular arrays. Rev. Geophysics Space Physics 18, 789–812.

    Article  Google Scholar 

  • Brillinger, D. R. (1966). Discussion. J. R. Statist. Soc. B 28, 294.

    Google Scholar 

  • Brillinger, D. R. (1972). The spectral analysis of stationary interval functions. In Proc. Sixth Berkeley Symp. Math. Stat. Prob. (Eds. L. M. Le Cam, J. Neyman, E. L. Scott), University of California Press, Berkeley, pp. 483–513.

    Google Scholar 

  • Brillinger, D. R. (1973). Estimation of the mean of a stationary time series by sampling. J. Appl. Prob. 10, 419–431.

    Article  MathSciNet  MATH  Google Scholar 

  • Brillinger, D. R. (1975). Statistical inference for stationary point processes. In Stochastic Processes and Related Topics, Vol. 1 (Ed. M. L. Puri), Academic Press, New York, pp. 55–99.

    Google Scholar 

  • Brillinger, D. R. (1979). Analyzing point processes subjected to random deletions. Canadian J. Stat. 7, 21–27.

    Article  MathSciNet  MATH  Google Scholar 

  • Brillinger, D. R. (1981). Time Series: Data Analysis and Theory. Holden-Day, San Francisco.

    MATH  Google Scholar 

  • Brillinger, D. R. (1982). Asymptotic normality of finite Fourier transforms of stationary generalized processes. J. Multivariate Anal. 12, 64–71.

    Article  MathSciNet  MATH  Google Scholar 

  • Brillinger, D. R., Bryant, H. L. Jr. and Segundo, J. P. (1976). Identification of synaptic interactions. Biol. Cybernetics 22, 213–228.

    Article  MATH  Google Scholar 

  • Cox, D. R. and Lewis, P. A. W. (1966). The Statistical Analysis of Series of Events. Methuen, London.

    MATH  Google Scholar 

  • Dunsmuir, W. and Robinson, P. M. (1981). Estimation of time series models in the presence of missing data. J. Amer. Statist. Assoc. 76, 560–568.

    MATH  Google Scholar 

  • Good, I. J. and Gaskins, R. A. (1972). Global nonparametric estimation of probability densities. Virginia J. Science 23, 171–193.

    MathSciNet  Google Scholar 

  • Grandell, J. (1976). Doubly Stochastic Poisson Processes. Springer, Berlin.

    MATH  Google Scholar 

  • Grenander, U. (1981). Abstract Inference. Wiley, New York.

    MATH  Google Scholar 

  • Hannan, E. J. (1971). Non-linear time series regression. J. Appl. Prob. 8, 767–780.

    Article  MathSciNet  MATH  Google Scholar 

  • Hinich, M. J, (1982). Estimating signal and noise using a random array. J. Acoust. Soc. Am. 71, 97–99.

    Article  MATH  Google Scholar 

  • Jones, R. H. (1971). Spectrum estimation with missing observations. Ann. Inst. Stat. Math. 23, 387–398.

    Article  MATH  Google Scholar 

  • Kempthorne, O. (1962). The Design and Analysis of Experiments. Wiley, New York.

    Google Scholar 

  • Kimeldorf, G. and Wahba, G. (1971). Some results on Tchebycheffian spline functions. J. Math. Anal. Applic. 33, 82–95.

    Article  MathSciNet  MATH  Google Scholar 

  • Lee, W. H. K. and Brillinger, D. R. (1979). On Chinese earthquake history—an attempt to model an incomplete data set by point process analysis. Pageoph. 117, 1229–1257.

    Article  Google Scholar 

  • Masry, E. (1978). Poisson sampling and spectral estimation of continuous-time processes. IEEE Trans. Inf. Theory IT-24, 173–183.

    Article  MathSciNet  MATH  Google Scholar 

  • Mohr, H. (1977). Structure and Significance of Science. Springer, New York.

    Book  Google Scholar 

  • Niemi, H. (1978). Stationary vector measures and positive definite translation invariant bimeasures. Ann. Acad. Sci. Fenn. Ser. A 4, 209–226.

    MathSciNet  Google Scholar 

  • Parzen, E. (1970). Statistical inference on time series by RKHS methods. In Proc. 12th Biennial Seminar Canadian Math. Congress (Ed. R. Pyke), Canadian Math. Cong., Montreal, pp. 1–38.

    Google Scholar 

  • Parzen, E. (1980). Comment. Amer. Stat. 34, 78–79.

    Article  Google Scholar 

  • Roberts, J. B. and Gaster, M. (1980). On the estimation of spectra from randomly sampled signals: a method of reducing variability. Proc. Roy. Soc. London 371, 235–258.

    Article  MathSciNet  Google Scholar 

  • Schwartzchild, M. (1979). New observation-outlier-resistant methods of spectrum estimation. Ph.D. Thesis (Statistics), Princeton University.

    Google Scholar 

  • Tukey, J. W. (1980). Can we predict where “time series” should go next? In Directions in. Times Series (Eds. D. R. Brillinger and G. C. Tiao), Inst. Math. Stat., Hayward, pp. 1-31.

    Google Scholar 

  • Vapnik, V. (1982). Estimation of Dependencies Based on Empirical Data. Springer, New York.

    Google Scholar 

  • Wahba, G. (1981). Constrained regularization for ill posed linear operator equations, with applications in meteorology and medicine. Proc. Third Purdue Symp. on Stat. Decision Theory (Eds. S. S. Gupta and J. O. Berger).

    Google Scholar 

  • Whittle, P. (1953). Estimation and information in stationary time series. Ark. Math. Astron. Fys. 2, 423–434.

    Article  MathSciNet  MATH  Google Scholar 

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© 1984 Springer-Verlag Berlin Heidelberg

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Brillinger, D.R. (1984). Statistical Inference for Irregularly Observed Processes. In: Parzen, E. (eds) Time Series Analysis of Irregularly Observed Data. Lecture Notes in Statistics, vol 25. Springer, New York, NY. https://doi.org/10.1007/978-1-4684-9403-7_3

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  • DOI: https://doi.org/10.1007/978-1-4684-9403-7_3

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-387-96040-1

  • Online ISBN: 978-1-4684-9403-7

  • eBook Packages: Springer Book Archive

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